Library Science I - For Class FA / HSC - Part 1 (Arts / General Group) - Model papers 2020 -2021

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Library Science I
For Class XI (Arts / General Group)
Model papers 2020 -2021

SOURCE: Board Of Intermediate Education Karachi

Psychology I - For Class FA / HSC - Part 1 (Arts / General Group) - Model papers 2020 -2021

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Psychology I
For Class XI (Arts / General Group)
Model papers 2020 -2021

SOURCE: Board Of Intermediate Education Karachi

Psychology II - For Class FA / HSC - Part 2 (Arts / General Group) - Model papers 2020 -2021

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Psychology II
For Class XII (Arts / General Group)
Model papers 2020 -2021

SOURCE: Board Of Intermediate Education Karachi

Education II - For Class FA / HSC - Part 2 (Arts / General Group) - Model papers 2020 -2021

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Education II
For Class XII (Arts / General Group)
Model papers 2020 -2021

SOURCE: Board Of Intermediate Education Karachi

Education I - For Class FA / HSC - Part 1 (Arts / General Group) - Model papers 2020 -2021

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Education I
For Class XI (Arts / General Group)
Model papers 2020 -2021

SOURCE: Board Of Intermediate Education Karachi

Mathematics For Class X Science - Unit 15: TRIGONOMETRY- Fill In The Blanks And Multiple Choice Questions (MCQs)

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UNIT 15: TRIGONOMETRY
Fill In The Blanks And Multiple Choice Questions (MCQs)

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12. Sin 20° = sin (90° - 70°) = cos 70°.
13. Cos 10° = cos (90° - 80°) = sin 80°.
14. Tan 40° = tan (90° - 50°) = cot 50°.
15. Sec 80° = (90° - 10°) = cosec 10°.
16. Cosec 10° = sec 80°.
17. Tan 20° = cot 70°.
18. 1 + tan² θ = sec² θ.
19. Cosec 60° = (90° - 30°) = sec 30°.
20. Cos 20° = sin 70°.
21. Cos 80° = sin 10°.
22. Tan² θ + 1 = sec² θ.
23. Sin 30° = cos 60°.
24. 1 + tan² 45° = sec² 45°.
25. Sin θ . sec θ = tan θ.
26. Cosec 30° = 2.
Special thanks to Sir Sajjad Akber Chandio

Mathematics For Class IX Science - Unit 03: LOGARITHMS - Fill In The Blanks And Multiple Choice Questions (MCQs)

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Unit 03: LOGARITHMS
Fill In The Blanks And Multiple Choice Questions (MCQs)

1. The characteristics of log 0.00226 is 3.
2. If log_x81 = 4, then x = 3.
3. The natural logarithm has the base e.
4. The characteristics of log 0.08595 is 2.
5. The characteristics of log 8595 is 3.
6. If log₇x = 2, the value of x is 7² = x.
7. The scientific notation of 756837 is 7.56837 x 10⁵.
8. If log_a16 = 4, a = 2.
9. The logarithm from of 2⁵ = 32 is log₂32 = 5.
10. The characteristics of log 6.67 x 10^-11 is 11.
11. log_a ^x3y/_z² = 3log_ax + log_ay - 2log_az.
12. If log₁₀1000 = y, the value of y will be 3.
13. The characteristics of log 0.00234 is 3.
14. If log₄x = -³/₂ = ¹/₈.
15. If log_x32 = 5, x = 2.
16. Logarithms were introduced by Abu Muhammad Musa Al-Khwarizmi.

Special thanks to Sir Sajjad Akber Chandio

Mathematics For Class IX Science - Unit 04: ALGEBRAIC EXPRESSION - Fill In The Blanks And Multiple Choice Questions (MCQs)

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Unit 04: ALGEBRAIC EXPRESSION
Fill In The Blanks And Multiple Choice Questions (MCQs)

1. (7a + 5) (7a - 5) = 49a² - 25. [Hint: (a² - b² = (a-b)(a+b)]
2.(a + 3b)² = a² + 6ab + 9b².
3. (3a - 2b)² = 9a² - 12ab + 4b².
4. (3a³ + b³)³ = 27a⁹ + 27a⁶b³ + 9a³b⁶ + 9b⁹
5. (p - q)³ = p³ - 3p²q + 3pq² - q³.
6.(2a² - 5y² - 3z²)² = 4a⁴ + 25y⁴ + 9z⁴ - 20a²y² + 30y²z² - 12z²a².
7. (x + 2) (x + 5) = x² + 7x + 10.
8. (2l + 3m²) - (2l - 3m²)² = 24lm².
9. The polynomial expression x² + 7x + 3 w.r.t the term is called trinomial.
10. The degree of polynomial x² + xy² + y is 3.
11. The algebraic expression 2a³y + 4ay² -5a² y³ in descending order w.r.t y is -5a² y³ + 4ay² + 2a³y.
12. The value of x - y - xy , if x = 1, y = 1 is 1.
13. (a + b)² + (a - b)² = 2a² + 2b²,
14. if x + y = 8, xy = 15. Find x² +y² = 34.
15. x⁴ + 64 can made a perfect square 16x².
16. if x³ + 4x² - 7x + 3 is divided by x - 1 then remainder is 1.
17. (a - b + c)² = a² - b² + c² - 2ab - 2bc + 2ca
18. (x - 6) (x - 4) = x² - 10x + 24.
19. If a + b = 2 and a - b = 2 then value of a² + b² is 4.

20. (√ x + √ y) (√ x - √ y) = (x - y)
21. (x - y)³ = x³ - y³ + 3x²y - 3xy².

Special Thanks To Sir Sajjad Akber Chandio

Mathematics For Class IX Science - Unit 07 - MATRICES - Fill In The Blanks And Multiple Choice Questions (MCQs)

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Unit 07: MATRICES
Fill In The Blanks And Multiple Choice Questions (MCQs)

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UNIT 7: Matrices

1. The arrangement of matrix R x C (Row x Column).
2. The matrix were introduced by Arther Kelly in 1858.
3. The number of row and column are not equal in matrix is called rectangular matrix. (R ≠ C ).
4. If a matrix has only one column is called column matrix.
5. If a matrix has only one row is called row matrix.
6. The number of row and column are equal is called square matrix.
7. If the matrix has all zero elements is called zero matrix or null matrix.

29. (A x B)^t = B^t x A^t
30. (A^t)^t = A
31. By distributive property of multiplication matrix over subtraction A(B-C) = AB - AC
32. If the value of determinant of matrix is 0 (zero), the matrix is called a /an singular matrix.
33. If the value of determinant of matrix is 1 or greater than 1 or less than 1, the matrix is called non - singular matrix.
34. The multiplicative inverse of a - b is ¹/_{a -b}
35. The multiplicative inverse of ¹/_a+b is a+b.
36. The multiplicative inverse of  ¹/_-2 = -2.
37. If rows and columns are equal the matrix is singular matrix.
38. If rows and column are not equal, the matrix is non singular matrix.

Special thanks to Sir Sajjad Akber Chandio

Mathematics For Class IX Science - Unit 01 - SETS - Fill In The Blanks And Multiple Choice Questions (MCQs)

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Unit 01: SETS
Fill In The Blanks And Multiple Choice Questions (MCQs)

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UNIT 1: SETS

1. The Cartesian product of set A and B is written as A x B.
2. {0, 1, 2, 3, 4, 5..........} is the set of whole numbers.
3. (A')' = A
4. A set which contains all the sets under consideration is called universal set.
5. Set is the collection of well-defined and distinct objects.
6. By associative property of intersection A ∩ (B ∩ C) = (A ∩ B) ∩ C.
7. Anything belongs to a set is called element of set.
8. Set of three prime number is {2, 3, 5}.
9. A = {1, 2, 4, 6, 8} , B = {1, 3, 5, 7, 9}. Then AUB = { 1, 2, 3, 4, 5, 6, 7, 8, 9}
10. A = {1, 2, 4, 6, 8} , B = {1, 3, 5, 7, 9}. Then A∩B = {1}
11. A = {2, 4, 6, 8, 10}, B = {1, 3, 5, 7, 10}. Then A - B = {2, 4, 6, 8}
12. A = {2, 4, 6, 8, 10}, B = {1, 3, 5, 7, 10}. Then B - A = {1, 3, 5, 7}
13. U = {1, 2, 3, ..... 10} , A = {2, 4, 6, 8}. Then A' = U - A
14. U = {1, 2, 3, ..... 10} , A = {2, 4, 6, 8}. Then A' = {1, 3, 5, 7, 9, 10}
15. A = {1, 2, 3, 4} B = {2, 3, 8}, A∆B = {1, 4, 8}
16. The set A = {1, 3, 5, 7 .....} is closed with respect to multiplication.
17. A set is finite = {1, 2, 3, 4, 5, 6, 7}, {-1, -2, -3, -4, -5, -6, -7}
18. Infinite set = {1, 2, 3......}, {-1, -2, -3......}
19. A set is equivalent denoted by = A ~ B.
20. A set of A is subset of set B = A ⊆ B.
21. The set of all possible subset of a set is called power set.
22. If n (A) = 10 then n [P (A)] = 1024.
(Hint: (For Power set, 'n' is the number of elements of set A.)
[P(A)] = 2ⁿ = 2¹⁰ = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1024.
∴ n [P (A)] = 1024)
23. If a set have four variable then subset is 16.
24. If A = {a, b} then subset are 4.
25. I is a / an rational number.
26. (3, -4) lie on 4^th quadrant - (forth or  VI).
27. (-5, -6) lie on 3^rd quadrant - (third or III).
28. (7, 8) lie on 1^st quadrant - (first or I).
29. (-9, 10) lie on 2^nd quadrant - (second or II).
30. (0, 4) lie on y-axis.
31. (-5, 0) lie on x-axis.
32. A binary relation from a set A to B is subset A X B.
33. Domain is denoted by D(x) and Range are denoted by R(y).
34. {1, 2}, {3, 4}, {5, 6}
Domain = {1, 3, 5}
Range = (2, 4, 6}
35. A = {2, 4}, B = {a, b} then A X B = {(2, a), (2, b) , (4, a) (4, b)}
36. (B')' ⇒ B = {2, 4, 6, 8}, U={1, 2, ........ 10} = {2, 4, 6, 8}
37. Collection of distinct objects which are called elements.
38. A set with no element is called Null set or Empty set.
39. The null set is denoted by { ∅ }
40. The empty set is denoted by { }.
41. A ∆ B = (AUB) - (A∩B)

Special Thanks to: Sir Sajjad Akber Chandio